For own good or to prove something to other people?

I think I have a thought that I am the least smart person in my family. I’m the only one with an art studies background who doesn’t have knowledge on how to start and run a business. My parents told me last year, “We did not think you would succeed,” and I think they still believe that I m not capable of doing things and being successful. I know that because of their attitude towards me all my life. I have been thinking that I’m not capable too. Of course, I m working on changing his thought. But my question is am I doing things (I started my company 6 years ago, moved to Japan, started my own brand, etc.) to prove to other people that I can do great things or am I doing them just because I love it? I’m lucky to be doing what I love to do, but I’m inventing my job everyday and, most of the time, it feels scary and I get very anxious. I know anxiety is normal, but I’m wondering if I’m not pushing myself too much and for the wrong reasons (for others and not for me).

How can I find that out? How can I find out whether I’m doing it only for me, for my own good?

Thank you!